Assous, F., Ciarlet, P., Labrunie, S. and Lorenghel, S. (2001) The Singular Complement Method. In Debit, N., Garbey, M., Hoppe, R., Priaux, J., Keyes, D. and Kuznetsov, Y., Eds., Thirteenth International Conference on Domain Decomposition Methods, Institut Elie Cartan, Villers-ls-Nancy, 159-187. - References

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Assous, F., Ciarlet, P., Labrunie, S. and Lorenghel, S. (2001) The Singular Complement Method. In: Debit, N., Garbey, M., Hoppe, R., Périaux, J., Keyes, D. and Kuznetsov, Y., Eds., Thirteenth International Conference on Domain Decomposition Methods, Institut Elie Cartan, Villers-lès-Nancy, 159-187.

has been cited by the following article:

TITLE: A Full Predictor-Corrector Finite Element Method for the One-Dimensional Heat Equation with Time-Dependent Singularities

AUTHORS: Jake L. Nkeck

KEYWORDS: Singularities, Finite Element Methods, Heat Equation, Predictor-Corrector Algorithm

JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.4, April 30, 2024

ABSTRACT: The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent singularities on the one-dimensional heat equation. The method is based on a Fourier decomposition of the solution and an extraction formula of the coefficients of the singularities coupled with a predictor-corrector algorithm. The method recovers the optimal convergence rate of the finite element method on a quasi-uniform mesh refinement. Numerical results are carried out to show the efficiency of the method.

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